Tutorial 2 — Spectroscopy: AB Pic b

Tutorial 2 — Spectroscopy: AB Pic b#

What you’ll learn: Fitting a medium-resolution K-band spectrum with ForMoSA v2.0. Compared to Tutorial 1 (photometry), spectroscopy adds resolution adaptation — the model grid must be convolved to match your instrument’s spectral resolution — and allows you to constrain the companion’s radial velocity.

Target: AB Pictoris b — a young (~30 Myr), directly-imaged planetary-mass companion at ~50 pc orbiting the debris-disk star AB Pic. It is one of the benchmarks for atmosphere retrieval codes because of its well-characterised orbit and known distance.

Data: VLT/SINFONI K-band spectrum (R ≈ 4000, λ = 2.0–2.45 µm). Published in Palma-Bifani et al. (2023, A&A, 670, A90).

Grid: BT-Settl (same grid downloaded in Tutorial 1)

Estimated runtime:

  • Grid adaptation: < 30 s

  • Nested sampling (200 live points, nestle): ~3 min

References: Palma-Bifani et al. (2023, A&A, 670, A90)

Section 0: Setup#

Run these four cells before anything else. They check your environment, create the working directories, download the observation data, and download the model grid.

[4]:

# Environment check
import sys
try:
    import ForMoSA
    print(f"ForMoSA {ForMoSA.__version__} — OK")
except ImportError:
    raise ImportError("pip install ForMoSA && conda install dask netCDF4 bottleneck")
print(f"Python {sys.version.split()[0]}")

ForMoSA 2.0.0 — OK
Python 3.11.13

[5]:

# Workspace setup
from pathlib import Path
TUTORIAL_DIR = Path(".").resolve()
for d in ["data", "adapted_grid", "results", "grid"]:
    (TUTORIAL_DIR / d).mkdir(exist_ok=True)
print(f"Working directory: {TUTORIAL_DIR}")

Working directory: /Users/rajpoot/Karmabhumi/Packages/ForMoSA/docs/tutorials/spectroscopy/abpicb

[6]:

# Data download + validation
import urllib.request
from astropy.io import fits

DATA_FILE = TUTORIAL_DIR / "data" / "ABPicb_SINFONI_K.fits"
DATA_URL  = (
    "https://github.com/exoAtmospheres/ForMoSA/releases/download/"
    "tutorial-data-v1/ABPicb_SINFONI_K.fits"
)

if not DATA_FILE.exists():
    print("Downloading observation data...")
    urllib.request.urlretrieve(DATA_URL, DATA_FILE)
    print("Done.")
else:
    print(f"Data already present: {DATA_FILE.name}")

# Validate required data keys. Support two FITS layouts:
# 1) Multiple HDUs named WAV/FLX/ERR/...
# 2) A single BINTable HDU with columns WAV/FLX/ERR/...
REQUIRED = {"WAV", "WAVE_UNIT", "FLX", "ERR", "FAC", "INS", "RES"}
with fits.open(DATA_FILE) as hdul:
    ext_names = {hdu.name.upper() for hdu in hdul[1:] if getattr(hdu, "name", None)}

    # Find first table HDU with columns, if any
    table_hdu = next(
        (hdu for hdu in hdul[1:] if hasattr(hdu, "columns") and hdu.columns is not None),
        None,
    )
    table_cols = ({name.upper() for name in table_hdu.columns.names} if table_hdu is not None else set())

# Prefer table-column validation when present; otherwise validate extension names
available = table_cols if table_cols else ext_names
missing = REQUIRED - available
if missing:
    mode = "table columns" if table_cols else "FITS extensions"
    raise RuntimeError(
        f"Missing required {mode}: {sorted(missing)}. "
        f"Found: {sorted(available)}"
    )

print("\nValidation source:", "BINTable columns" if table_cols else "FITS extensions")
print("Required keys (marked ✓):")
for name in sorted(available):
    mark = "✓" if name in REQUIRED else " "
    print(f"  {mark} {name}")
print("\nAll required keys present — data is valid.")

Data already present: ABPicb_SINFONI_K.fits

Validation source: BINTable columns
Required keys (marked ✓):
  ✓ ERR
  ✓ FAC
    FILT
  ✓ FLX
  ✓ INS
  ✓ RES
  ✓ WAV
  ✓ WAVE_UNIT

All required keys present — data is valid.

[7]:

# Grid download
# The full BT-Settl grid is ~1 GB. Once downloaded, keep it —
# it works for all ForMoSA tutorials and your own science.
import urllib.request

GRID_FILE = TUTORIAL_DIR / "grid" / "BT-Settl.nc"
GRID_URL  = "https://drive.usercontent.google.com/download?id=1wvf4A-DupdVnYIpK_HmHE-fobqnYtvEz&export=download&confirm=t"

# Override GRID_FILE here if you already have the grid elsewhere:
# GRID_FILE = Path("/path/to/your/BT-Settl.nc")

if not GRID_FILE.exists():
    print("Downloading BT-Settl model grid (~1 GB). This takes a few minutes.\n")
    try:
        from tqdm import tqdm
        class _Progress(tqdm):
            def update_to(self, b=1, bs=1, ts=None):
                if ts: self.total = ts
                self.update(b * bs - self.n)
        with _Progress(unit="B", unit_scale=True, desc="BT-Settl.nc") as t:
            urllib.request.urlretrieve(GRID_URL, GRID_FILE, reporthook=t.update_to)
    except ImportError:
        def _progress(count, bs, total):
            pct = min(100, count * bs / total * 100)
            print(f"\r  {pct:.1f}%  {count*bs/1e6:.1f}/{total/1e6:.1f} MB",
                  end="", flush=True)
        urllib.request.urlretrieve(GRID_URL, GRID_FILE, reporthook=_progress)
        print()
    print(f"\nSaved: {GRID_FILE}")
else:
    print(f"Grid already present: {GRID_FILE.name}")

import xarray as xr
grid = xr.open_dataset(GRID_FILE, decode_cf=False)
par_names = grid.attrs.get("par", [])
par_units = grid.attrs.get("unit", [])
print(f"\nGrid dimensions: {dict(grid.sizes)}")
for i, (key, name, unit) in enumerate(zip(["par1", "par2", "par3", "par4"],
                                           par_names or ["par1","par2","par3","par4"],
                                           par_units or ["","","",""])):
    if key in grid.coords:
        vals = grid[key].values
        print(f"  {name} {unit}: {vals[0]:.1f} → {vals[-1]:.1f}  ({len(vals)} points)")

# Display the grid content in a notebook
# Click on the data repo icon (on the right) to show the full content if needed
grid

Grid already present: BT-Settl.nc

Grid dimensions: {'wavelength': 1161983, 'par1': 22, 'par2': 7}
  teff (K): 1200.0 → 2900.0  (22 points)
  logg (dex): 2.5 → 5.5  (7 points)

[7]:

<xarray.Dataset>
Dimensions:     (wavelength: 1161983, par1: 22, par2: 7)
Coordinates:
  * wavelength  (wavelength) float64 0.3001 0.3001 0.3001 ... 30.0 30.0 30.0
  * par1        (par1) float64 1.2e+03 1.3e+03 1.4e+03 ... 2.8e+03 2.9e+03
  * par2        (par2) float64 2.5 3.0 3.5 4.0 4.5 5.0 5.5
Data variables:
    grid        (wavelength, par1, par2) float64 ...
Attributes:
    key:      ['par1', 'par2']
    par:      ['teff', 'logg']
    title:    ['Teff', 'log(g)']
    unit:     ['(K)', '(dex)']
    res:      [ 60003.04331194  60004.04327964  60005.04321604 ... 149994.483...

Section 1: The science#

Spectroscopy vs photometry#

Photometry gives you broad-band colours. A medium-resolution spectrum gives you the shape of molecular absorption features — CO overtone bands at 2.29–2.45 µm, H₂O bands, and more. This makes spectroscopy far more sensitive to Teff and log g, and crucially, it allows you to measure the radial velocity (RV) of the companion by cross-correlating the observed features against the model.

Why no vsini?#

To measure rotational broadening (vsini) reliably, you need R > 50,000 so that individual rotational lines are resolved. SINFONI K-band delivers R ≈ 4000 — enough for molecular features but not for vsini. We therefore fit rv but not vsini. (Tutorial 3 covers vsini with VLT/HiRISE at R ≈ 140,000.)

AB Pic b#

AB Pic b is a ~13 MJup companion at a projected separation of ~275 au, co-moving with the β Pic moving group (age ≈ 20–30 Myr). Its low surface gravity and warm temperature make it an L-type object with prominent CO and H₂O absorption. Literature values: Teff ≈ 1700 K, log g ≈ 4.0, d = 50.1 pc (Hipparcos).

Section 2: Inspect the data#

[8]:

from astropy.table import Table
import matplotlib.pyplot as plt

table = Table.read(DATA_FILE, format="fits")
wav  = table["WAV"].data.astype(float)       # wavelength (µm)
flx  = table["FLX"].data.astype(float)       # flux (W/m²/µm)
err  = table["ERR"].data.astype(float)       # 1-σ uncertainty
fac  = table["FAC"].data                     # facility names
ins  = table["INS"].data                     # instrument names
res  = table["RES"].data.astype(float)       # spectral resolution R = λ/Δλ

print(f"Wavelength range : {wav.min():.4f} – {wav.max():.4f} µm")
print(f"Number of points : {len(wav)}")
print(f"Resolution R     : {res.mean():.0f} ± {res.std():.0f}  (mean ± std)")

fig, ax = plt.subplots(figsize=(8, 4), sharex=True, dpi=300)
ax.plot(wav, flx, color="C0", lw=0.8, label="AB Pic b  (SINFONI K)")
ax.fill_between(wav, flx - err, flx + err, color="C1", alpha=0.2)
ax.set_ylabel(r"Flux (W m$^{-2}$ µm$^{-1}$)")
ax.legend()
ax.grid(alpha=0.3)
plt.tight_layout();

Wavelength range : 1.9530 – 2.4472 µm
Number of points : 2018
Resolution R     : 5090 ± 0  (mean ± std)
../../../_images/tutorials_spectroscopy_abpicb_tutorial_spectroscopy_8_1.png

Section 3: Configure the analysis#

Part A: Setting up the configurations#

ForMoSA v2.0 uses four Python dataclasses to configure a run. Each dataclass groups related settings — you only need to set the ones that differ from the defaults.

Dataclass

Controls

ConfigPath

File paths (observation, grid, output directories)

ConfigAdapt

How the grid is resampled to match the observations

ConfigInversion

Wavelength fitting window, nested sampling algorithm

ConfigParameters

Prior on each free parameter

Config_NS

Settings for Nested Sampling Algorithms

 
[9]:

from ForMoSA.config.global_config import ConfigPath, ConfigAdapt, ConfigInversion, ConfigParameters, Config_NS, ConfigPyMultiNest

# ──────────────────────────── Paths ────────────────────────────
config_path = ConfigPath(
    observation_path=[str(DATA_FILE)],
    adapt_store_path=str(TUTORIAL_DIR / "adapted_grid"),
    result_path=str(TUTORIAL_DIR / "results"),
    model_path=str(GRID_FILE),
)

# ────────────────────────── Adaptation ──────────────────────────
config_adapt = ConfigAdapt()

# you can also try different adaptation settings to see how they affect the fit. For example:
# res_cont=500 tells ForMoSA to remove the continuum using a low-pass filter
# at R=500 before comparing model to data. This removes broad-band slope
# differences and lets the fit focus on molecular features.
# config_adapt = ConfigAdapt(
#     res_cont = 500,                 # enable continuum removal at R=500
#     wav_cont = ["2.0, 2.45"],       # only use K-band for continuum fit (same as wav_fit below)
# )


# ─────────────────────────── Inversion ──────────────────────────
config_inversion = ConfigInversion(
    wav_fit   = ["2.0, 2.45"],
    ns_algo   = "pymultinest",           # nested sampling algorithm to use
    npoints   = 100,                # more live points for better posterior sampling
    logL_type = ["chi2"],
)

# ────────────────────────── Parameters ──────────────────────────
# Syntax for priors: ["type", "min", "max"] or ["constant", "value"]
# par1 = Teff (K), par2 = log g (dex) — read from grid attributes above
config_params = ConfigParameters(
    par1 = ["uniform", "1200", "2900"],     # Teff (K)
    par2 = ["uniform", "2.5", "5.5"],       # log g (dex)
    rv   = ["uniform", "-100", "100"],      # radial velocity (km/s)
)

# ───────────────────── Nested Sampling Algo ───────────────────────
# Initialize the nested sampling configuration with the chosen algorithm (here, pymultinest)
config_ns = Config_NS(pymultinest=ConfigPyMultiNest())


# Display the configuration for verification
print("Configuration:")
print(f"  wav_fit : {config_inversion.wav_fit[0]} µm")
print(f"  Free    : {config_params.par1[1]} - {config_params.par1[2]} (Teff), {config_params.par2[1]} - {config_params.par2[2]} (log g), {config_params.rv[1]} - {config_params.rv[2]} (rv)")

Configuration:
  wav_fit : 2.0, 2.45 µm
  Free    : 1200 - 2900 (Teff), 2.5 - 5.5 (log g), -100 - 100 (rv)

Saving the configuration for later reference#

[10]:

# Saving the configuration for later reference
from ForMoSA.config.global_config import ConfigGenerator

# Initialize the generator
generator = ConfigGenerator()

# Create a dictionary of your configuration objects
generator.config.update({
    "config_path": config_path,
    "config_adapt": config_adapt,
    "config_inversion": config_inversion,
    "config_parameters": config_params,
    "config_ns": config_ns,
})

# Save to an .ini file
generator.save(path=TUTORIAL_DIR, name="spectro_config.ini")

INFO         Save config to path /Users/rajpoot/Karmabhumi/Packages/ForMoSA/docs/tutorials/spectroscopy/abpicb

Loading of the configuration file#

If you are just using the configuration file, then you have to load it first so that it can be passed to all algorithms. The Nested Sampling class will use only the parameters relevant to the algorithm you are using.

[11]:

from ForMoSA.config.global_config import ConfigLoader, Config_NS

# Load the configuration from the .ini file we just saved
cfg = ConfigLoader(str(TUTORIAL_DIR/'spectro_config.ini'))
sections = cfg.load()

# Extract the individual configuration sections
config_path = sections.get("config_path")
config_adapt = sections.get("config_adapt")
config_inversion = sections.get("config_inversion")
config_params = sections.get("config_parameters")

# Initialize Config_NS (required for nested sampling) with the loaded configuration sections
config_ns = Config_NS(
                nestle=cfg.config['config_nestle'],
                pymultinest=cfg.config['config_pymultinest'],
                ultranest=cfg.config['config_ultranest']
            )

INFO         Config file loaded

Step B: Setting up the Analysis object#

Analysis object is the main interface to run the ForMoSA using the provided configuration. It allows you to run the adaptation and inversion steps, or skip them if already done, and proceed directly to plotting results.

NOTE: Here we create the main analysis class. For the purpose of not overcharging the notebook, we use log_level = ‘error’.

The different options are:

  • ‘info’: basic information

  • ‘debug’: basic information + additional debugging information

  • ‘warning’: only warning messages

  • ‘error’: only error messages, so typically no message unless you have an error in the code

  • ‘critical’: same thing as ‘error’ but for critical ones

  • ‘off’ or None: no logging

[12]:

from ForMoSA import Analysis

# If this is the first time you are adapting your model grid, or if you need to re-adapt it, set adapted = False
# If you have already adapted your model grid, set adapted = True
adapted = False

# If you want to perform the fit, set fitted = False
# If you only want to generate plots, set fitted = True
fitted = False

# Initialize the Analysis object with the loaded configuration sections and control flags
analysis = Analysis(config_path, adapted=adapted, fitted=fitted, log_level='error')

Section 4: Adapt the grid#

The grid is pre-computed at native model resolution. Before fitting, ForMoSA adapts it: it evaluates the model flux through your spectroscopic observation, producing a much smaller grid of model spectra that is directly comparable to your observations.

For spectroscopy, adaptation can take some time depending upon how big your grid is and how high the spectral resolution of your data is.

Set adapted=True on subsequent runs to skip this step and load the cached grid.

[13]:

if not adapted:
    # Adaptation convolves each model spectrum to match the SINFONI resolution
    # and resamples it onto the observed wavelength grid.
    print("Adapting grid (convolution + resampling)...")
    analysis.adapt(config_adapt, config_inversion)
    print("Done. Set adapted=True to skip on re-runs.")
else:
    print("Skipping adaptation. Set adapted=False to re-run.")

Adapting grid (convolution + resampling)...

BT-Settl_[Paranal]_[SINFONI]_Spectroscopic: 100%|██████████| 154/154 [00:07<00:00, 20.63model/s]

Done. Set adapted=True to skip on re-runs.

Section 5: Run the nested sampling fit#

Nested sampling explores the prior volume and computes the Bayesian evidence (log Z) alongside the posterior distributions. In this tutorial, we will use pymultinest to run with more live points. This requires pymultinest to be installed locally. If not, then check the installation page for the instructions.

The npoints=100 setting is a good starting point for a quick check. For publication-quality posteriors, use 300–500 live points.

[14]:

if not fitted:
    print(f"Running {config_inversion.ns_algo} with {config_inversion.npoints} live points...")
    analysis.nested_sampling(config_params, config_adapt, config_inversion, config_NS=config_ns)
    print("\nFit complete.")
else:
    print("Skipping fit. Set fitted=False to run the fit.")

Running pymultinest with 100 live points...
 *****************************************************
 MultiNest v3.10
 Copyright Farhan Feroz & Mike Hobson
 Release Jul 2015

 no. of live points =  100
 dimensionality =    3
 *****************************************************
 Starting MultiNest
 generating live points
 live points generated, starting sampling
Acceptance Rate:                        0.914634
Replacements:                                150
Total Samples:                               164
Nested Sampling ln(Z):              -5589.657900
Importance Nested Sampling ln(Z):   -1000.323229 +/-  0.996947
Acceptance Rate:                        0.858369
Replacements:                                200
Total Samples:                               233
Nested Sampling ln(Z):              -2970.624022
Importance Nested Sampling ln(Z):    -978.806982 +/-  0.997852
Acceptance Rate:                        0.788644
Replacements:                                250
Total Samples:                               317
Nested Sampling ln(Z):              -2320.951887
Importance Nested Sampling ln(Z):    -881.087683 +/-  0.998421
Acceptance Rate:                        0.759494
Replacements:                                300
Total Samples:                               395
Nested Sampling ln(Z):              -1859.578011
Importance Nested Sampling ln(Z):    -881.623562 +/-  0.998733
Acceptance Rate:                        0.733753
Replacements:                                350
Total Samples:                               477
Nested Sampling ln(Z):              -1598.781755
Importance Nested Sampling ln(Z):    -882.150531 +/-  0.998951
Acceptance Rate:                        0.686106
Replacements:                                400
Total Samples:                               583
Nested Sampling ln(Z):              -1424.081780
Importance Nested Sampling ln(Z):    -882.730825 +/-  0.999142
Acceptance Rate:                        0.668648
Replacements:                                450
Total Samples:                               673
Nested Sampling ln(Z):              -1259.451501
Importance Nested Sampling ln(Z):    -883.197321 +/-  0.999256
Acceptance Rate:                        0.625000
Replacements:                                500
Total Samples:                               800
Nested Sampling ln(Z):              -1133.118985
Importance Nested Sampling ln(Z):    -856.805203 +/-  0.999375
Acceptance Rate:                        0.603732
Replacements:                                550
Total Samples:                               911
Nested Sampling ln(Z):              -1057.936559
Importance Nested Sampling ln(Z):    -826.303046 +/-  0.993331
Acceptance Rate:                        0.587084
Replacements:                                600
Total Samples:                              1022
Nested Sampling ln(Z):              -1000.712316
Importance Nested Sampling ln(Z):    -802.473387 +/-  0.999511
Acceptance Rate:                        0.578807
Replacements:                                650
Total Samples:                              1123
Nested Sampling ln(Z):               -961.118679
Importance Nested Sampling ln(Z):    -799.586543 +/-  0.966846
Acceptance Rate:                        0.567261
Replacements:                                700
Total Samples:                              1234
Nested Sampling ln(Z):               -931.518472
Importance Nested Sampling ln(Z):    -800.123426 +/-  0.966864
Acceptance Rate:                        0.546249
Replacements:                                750
Total Samples:                              1373
Nested Sampling ln(Z):               -910.132675
Importance Nested Sampling ln(Z):    -786.103262 +/-  0.999635
Acceptance Rate:                        0.530152
Replacements:                                800
Total Samples:                              1509
Nested Sampling ln(Z):               -893.770151
Importance Nested Sampling ln(Z):    -780.647942 +/-  0.997231
Acceptance Rate:                        0.517977
Replacements:                                850
Total Samples:                              1641
Nested Sampling ln(Z):               -883.499867
Importance Nested Sampling ln(Z):    -781.189490 +/-  0.997257
Acceptance Rate:                        0.514874
Replacements:                                900
Total Samples:                              1748
Nested Sampling ln(Z):               -864.826809
Importance Nested Sampling ln(Z):    -781.496304 +/-  0.895744
Acceptance Rate:                        0.508565
Replacements:                                950
Total Samples:                              1868
Nested Sampling ln(Z):               -848.175397
Importance Nested Sampling ln(Z):    -781.001389 +/-  0.690604
Acceptance Rate:                        0.508906
Replacements:                               1000
Total Samples:                              1965
Nested Sampling ln(Z):               -835.425404
Importance Nested Sampling ln(Z):    -781.375746 +/-  0.655673
Acceptance Rate:                        0.510452
Replacements:                               1050
Total Samples:                              2057
Nested Sampling ln(Z):               -824.782825
Importance Nested Sampling ln(Z):    -781.394963 +/-  0.534669
Acceptance Rate:                        0.511152
Replacements:                               1100
Total Samples:                              2152
Nested Sampling ln(Z):               -812.151840
Importance Nested Sampling ln(Z):    -781.608316 +/-  0.434727
Acceptance Rate:                        0.513622
Replacements:                               1150
Total Samples:                              2239
Nested Sampling ln(Z):               -803.636806
Importance Nested Sampling ln(Z):    -781.582990 +/-  0.420066
Acceptance Rate:                        0.511727
Replacements:                               1200
Total Samples:                              2345
Nested Sampling ln(Z):               -797.521323
Importance Nested Sampling ln(Z):    -781.503042 +/-  0.346377
Acceptance Rate:                        0.513347
Replacements:                               1250
Total Samples:                              2435
Nested Sampling ln(Z):               -792.466818
Importance Nested Sampling ln(Z):    -781.587788 +/-  0.284499
Acceptance Rate:                        0.514444
Replacements:                               1300
Total Samples:                              2527
Nested Sampling ln(Z):               -789.395908
Importance Nested Sampling ln(Z):    -781.695580 +/-  0.234648
Acceptance Rate:                        0.515858
Replacements:                               1350
Total Samples:                              2617
Nested Sampling ln(Z):               -786.578159
Importance Nested Sampling ln(Z):    -781.795081 +/-  0.209050
Acceptance Rate:                        0.517178
Replacements:                               1400
Total Samples:                              2707
Nested Sampling ln(Z):               -784.655556
Importance Nested Sampling ln(Z):    -781.474728 +/-  0.166524
Acceptance Rate:                        0.516198
Replacements:                               1450
Total Samples:                              2809
Nested Sampling ln(Z):               -783.410051
Importance Nested Sampling ln(Z):    -781.304347 +/-  0.133262
Acceptance Rate:                        0.514580
Replacements:                               1500
Total Samples:                              2915
Nested Sampling ln(Z):               -782.587657
Importance Nested Sampling ln(Z):    -781.299044 +/-  0.108011
Acceptance Rate:                        0.515464
Replacements:                               1550
Total Samples:                              3007
Nested Sampling ln(Z):               -782.010497
Importance Nested Sampling ln(Z):    -781.269581 +/-  0.088298
Acceptance Rate:                        0.515464
Replacements:                               1600
Total Samples:                              3104
Nested Sampling ln(Z):               -781.582432
Importance Nested Sampling ln(Z):    -781.240086 +/-  0.075005
Acceptance Rate:                        0.512900
Replacements:                               1650
Total Samples:                              3217
Nested Sampling ln(Z):               -781.303768
Importance Nested Sampling ln(Z):    -781.259925 +/-  0.066105
Acceptance Rate:                        0.511740
Replacements:                               1700
Total Samples:                              3322
Nested Sampling ln(Z):               -781.124428
Importance Nested Sampling ln(Z):    -781.241714 +/-  0.060783
Acceptance Rate:                        0.511231
Replacements:                               1707
Total Samples:                              3339
Nested Sampling ln(Z):               -781.104342
Importance Nested Sampling ln(Z):    -781.240305 +/-  0.060210
  analysing data from RAW_.txt
 ln(ev)=  -780.80011038386397      +/-  0.36878937629917963
 Total Likelihood Evaluations:         3339
 Sampling finished. Exiting MultiNest

Fit complete.

Section 6: Results#

ForMoSA produces four diagnostic plots saved to results/:

File

Shows

corner.pdf

Posterior distributions and pairwise correlations

chains.pdf

Sample chains and weights (convergence check)

radar.pdf

Radar diagram of median ± 1σ for each parameter

best_fit.pdf

Best-fit model vs. observed data + residuals

 
[15]:

analysis.plot(analysis.ns.results, plot_native_model=False)
print(analysis.ns.results.summary(sigma=1))

======== Nested Sampling Summary ====================
LogZ = -780.800 ± 0.369

Posterior estimates (median ± 1 sigma interval)

Teff        :  1480.1777 -  1.4425 +  1.4013 [1478.7352, 1481.5790]  MAP=1479.5289
log(g)      :     2.7420 -  0.0160 +  0.0173 [2.7260, 2.7594]  MAP=2.7320
rv          :    20.6912 -  0.7133 +  0.9354 [19.9779, 21.6266]  MAP=20.9455
=====================================================
../../../_images/tutorials_spectroscopy_abpicb_tutorial_spectroscopy_24_1.png
../../../_images/tutorials_spectroscopy_abpicb_tutorial_spectroscopy_24_2.png
../../../_images/tutorials_spectroscopy_abpicb_tutorial_spectroscopy_24_3.png
../../../_images/tutorials_spectroscopy_abpicb_tutorial_spectroscopy_24_4.png

Section 7: Next steps#

  • Tutorial 3 — HCHR mode (AF Lep b): VLT/HiRISE at R ≈ 140,000. Introduces STAR_FLUX extension, high-contrast modeling, and vsini.

  • Tutorial 5 — Advanced plotting: Deep-dive into every ForMoSA plot and how to customise it for publication. Uses these results as input.